With the rapid development in today&rsquo / s technology, reliability and performance requirements on components of various mechanical systems, which tend to be much lighter and work under much more severe working conditions, dramatically increased. In general, analysis techniques based on simplified model of structural components with linearity assumption may provide time saving for solutions with reasonable accuracy. However, since most engineering structures are often very complex and intrinsically nonlinear, in some cases they may behave in a different manner which cannot be fully described by linear mathematical models, or linear treatments may not be applicable at all. In fact, some studies revealed that deviations in the modal properties of dynamic structures gathered from measured data are due to nonlinearities in the structure. Hence, in problems where accuracy is the primary concern, taking the nonlinear effects into account becomes inevitable. In this thesis, it is aimed to analyze the harmonic response characteristics of multi degree of freedom nonlinear structures having different type of nonlinearities. The amplitude dependencies of nonlinearities are modelled by using describing function method. To increase the accuracy of the results, effect of the higher order harmonic terms will be considered by using multi harmonic describing function theory. Mathematical formulations are embedded in a computer program developed in MATLAB&reg / with graphical user interface. The program gets the system matricies from the file which is obtained by using substructuring analysis in ANSYS&reg / , and nonlinearities in the system can easily be defined through the graphical user interface of the MATLAB&reg / program.

Current hydro-turbines aim to capture the immense energy available in tidal movements, however commonly applied technologies rely on principles more applicable in hydroelectric dams. Tidal stream currents, such as in Coastal Georgia, are not strong enough to make such turbines both efficient and economically viable. This research proposes a novel low-energy vortex shedding vertical axis turbine (VOSTURB) to combat the inefficiencies and challenges of hydro-turbines in low velocity free tidal streams. Some of the energy in tidal streams is extracted naturally from vortex shedding; as water streams past a bluff body, such as pier, low pressure vortices form alternatively on each side, inducing a rhythm of pressure differentials on the bluff body and anything in its wake. VOSTURB aims to capture this energy of the vortices by installing a hydrofoil subsequent to the bluff body. This foil, free to oscillate, translates the vortex energy into oscillatory motion, which can be converted into a form of potential energy. The presented research will act as a 'proof of concept.' It aims to assess such foil motion, or the ability of VOSTURB to capture vortex energy, and begin to assess the amount of tidal energy that can be theoretically harnessed. In this study a small scale model of VOSTURB, a cylindrical bluff body with a hammer shaped hydrofoil, was tested in a hydraulic flume for various mean flow speeds. Tangential accelerations of the foil's center of gravity were obtained through the use of an accelerometer. The acceleration data was analyzed utilizing Fourier analysis to determine the fundamental frequency of the wing oscillations. The available power to be harnessed from the oscillatory motion was then estimated utilizing this fundamental frequency. Ultimately it was found that the frequency of the VOSTURB foil oscillations corresponded highly with the theoretical frequency of vortex shedding for all moderate to high flow speeds. Low speeds were found to produce inconsistent and intermittent small oscillations. This signifies at moderate to high flow speeds, VOSTURB was able to transform some vortical energy into kinetic. The maximum average power obtained 8.4 mW corresponded to the highest flow velocity 0.27 m/s. Scaled to Rose Dhu prototype conditions this represented 50 W at a flow velocity of 0.95m/s, the maximum available at Rose Dhu. Although it was ascertained that VOSTURB could consistently capture some of the vortical energy; the percentage of which could not be calculated with certainty. Thus, the average kinetic power assessments of the foil were compared to the available power of the mean flow for each flow speed calculated by two methods: (1) over the foil's swept area; (2) the area of fluid displaced by the bluff body immediately in front of the foil. The maximum efficiency of the foil, found for the fastest flow speed was at 18% and 45% respectively. It was found that both average foil power, available flow power, and efficiency all decreased with a decrease in flow velocity. This study can serve as only a preliminary study for the effectiveness of VOSTURB as a hydro-turbine for tidal power. In the experiments, the foil was allowed to oscillate freely with little resistance. Future testing of VOSTURB needs to observe whether the vortex energy can overcome the resistive torque introduced by a generator to induce oscillatory motion as well as further optimize the foil design. While the testing in this project assesses the kinetic energy or power of the vortex shedding, this future testing will provide insight into the actual work that can actually be converted into potential energy or power. Complementing this research, both a Harmonic Analysis of Least Squares (HAMELS) and a Complex Empirical Orthogonal Function (CEOF) Analysis was conducted on available surface height and current velocity data separately from an available Regional Ocean Modeling System (ROMS) model of Coastal Georgia. Such analysis were conducted to observe spatial and temporal tidal patterns advantageous to a possible prototype installation of a tidal turbine such as VOSTURB. The more conventional HAMELS analysis, which isolates components of a signal with a certain frequency, identified temporal and spatial patterns attributed to tidal constituents. CEOF analysis, where major patterns of variance are identified not according to prescribed frequencies, was employed to identify any patterns possible not attributed to the tidal constituents. This study was also in part to observe whether the CEOF analysis could identify any patterns of tidal propagation that could not be resolved by the HAMELS analysis. The CEOF and HAMELS analysis of the surface height output produced very similar results: major modes of surface height variation due to the diurnal and semidiurnal tidal constituents propagating up the estuary. The CEOF results did not produce any additional information that could not be found through the HAMELS analysis of the constituents and presented such results in an arguably more convoluted manner. In addition, the surface height analysis provided no direct insight into areas more advantageous to tidal power. The CEOF analysis of the vector current velocity data however did provide some insight. The CEOF of the current data was able to isolate patterns of variance corresponding to the tidal constituents. However, the CEOF was also able to identify local 'hotspots' of high current magnitudes not resolved by HAMELS. These local areas of high current magnitudes, most likely due to changes in hydrodynamic conditions such as channel constrictions, are advantageous for tidal power applications. These general areas could serve as a starting point for the location selection process for a possible prototype installation of VOSTURB if the area was refined more. Ultimately for a prototype installation of VOSTURB, further experimentation and analysis is required for both the turbine design and placement, such as a power conversion methodology for the turbine and a more spatially resolute set of data to perform a CEOF analysis on. With these tasks completed, the prototype installation will be part of a larger effort between the Georgia Institute of Technology and the Girl Scouts of America to create completely sustainable "Eco-Village" on Rose Dhu Island, GA. With an extensive community outreach planned to educate the public, Rose Dhu, along with championing hydrokinetic energy, will serve as a paradigm for sustainable design and energy.

In flexible fitting, the high-resolution crystal structure of a molecule is deformed to optimize its position with respect to a low-resolution density map. Solving the flexible fitting problem entails answering the following questions: (A) How can the crystal structure be deformed? (B) How can the term "optimum" be defined? and (C) How can the optimization problem be solved? In this dissertation, we answer the above questions in reverse order. (C) We develop PFCorr, a non-uniform SO(3)-Fourier-based tool to efficiently conduct rigid-body correlations over arbitrary subsets of the space of rigid-body motions. (B) We develop PF2Fit, a rigid-body fitting tool that provides several useful definitions of the optimal fit between the crystal structure and the density map while using PFCorr to search over the space of rigid-body motions (A) We develop PF3Fit, a flexible fitting tool that deforms the crystal structure with a hierarchical domain-based flexibility model while using PF2Fit to optimize the fit with the density map. Our contributions help us solve the rigid-body and flexible fitting problems in unique and advantageous ways. They also allow us to develop a generalized framework that extends, breadth-wise, to other problems in computational structural biology, including rigid-body and flexible docking, and depth-wise, to the question of interpreting the motions inherent to the crystal structure. Publicly-available implementations of each of the above tools additionally provide a window into the technically diverse fields of applied mathematics, structural biology, and 3D image processing, fields that we attempt, in this dissertation, to span. / text

No description available.

Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.

Soit μ une mesure de probabilité borélienne sur SL m+1 (R) tel que le sous-groupe engendré par le support de μ est Zariski dense. Soit V une représentation irréductible de dimension finie de SL m+1 (R). D’après un théorème de Furstenberg, il existe une unique mesure μ-stationnaire sur PV et nous nous somme intéressés à la décroissance de Fourier de cette mesure. Le résultat principal de cette thèse est que la transformée de Fourier de la mesure stationnaire a une décroissance polynomiale. À partir de ce résultat, nous obtenons un trou spectral de l’opérateur de transfert, dont les propriétés nous permettent d’établir un terme d’erreur exponentiel pour le théorème de renouvellement dans le cadre des produits de matrices aléatoires. L’ingrédient essentiel est une propriété de décroissance de Fourier des convolutions multiplicatives de mesures sur R n , qui est une généralisation d’un théorème de Bourgain en dimension 1. Nous établissons cet ingrédient en utilisant un estimée somme produit de He et de Saxcé.Dans la dernière partie, nous généralisons un résultat de Lax et Phillips et un résultat de Hamenstädt sur la finitude des petites valeurs propres de l’opérateur de Laplace sur les variétés hyperboliques géométriquement finies. / Let μ be a Borel probability measure on SL m+1 (R), whose support generates a Zariski dense subgroup. Let V be a finite dimensional irreducible linear representation of SL m+1 (R). A theorem of Furstenberg says that there exists a unique μ-stationary probability measure on PV and we are interested in the Fourier decay of the stationary measure. The main result of the thesis is that the Fourier transform of the stationary measure has a power decay. From this result, we obtain a spectral gap of the transfer operator, whose properties allow us to establish an exponential error term for the renewal theorem in the context of products of random matrices. A key technical ingredient for the proof is a Fourier decay of multiplicative convolutions of measures on R n , which is a generalisation of Bourgain’s theorem on dimension 1. We establish this result by using a sum-product estimate due to He-de Saxcé. In the last part, we generalize a result of Lax-Phillips and a result of Hamenstädt on the finiteness of small eigenvalues of the Laplace operator on geometrically finite hyperbolic manifolds

Made available in DSpace on 2015-03-26T13:50:03Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2150977 bytes, checksum: 3411fdf85f685253ef23effd25ee9315 (MD5) Previous issue date: 2009-07-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study objective was to analyze the space distribution of components of the reference evapotranspiration (ETo) in Brazil and afterwards the weather variability by applying the technique of harmonic analysis, given for this was initially an analysis of variance, phase and amplitude for the present time (1980-2000), subsequently made a projection of future time (2080-2100), based on scenario A2 of intergovernmental panel to Climatic changes. The equation used was Penman-Monteith sampled by Food and Agriculture and Organization of the United Nations (FAO) 1998. The simulations were conducted with the clime regional model (MM5), attached to a model of potential vegetation (MVP). The results show that under the actual conditions the model presented good performance of the annual cycle when compared to the ERA-40 and CRU data. The aero dynamical and radioactive terms presented an annual cycle that is dominant in the Amazonian and Brazil's south regions, while in the southeast region the semester cycle has a higher notability. The biggest variations at ETo amplitude were identified in northeastern semiarid and in the Brazil's extreme south. The changes in ETo due to the global warmness were maximum at the Brazil's central region and in the Amazonian region. In future conditions, the annual cycle showed itself dominant in Brazil's greatest part, presenting dry and rainy well defined weathers. Still was observed that under global warmness conditions the variations of aerodynamic term become more important than the variations of the irradiative terms to the total ETo. / O objetivo do presente estudo foi analisar a distribuição espacial dos componentes da evapotranspiração de referência (ETo) no Brasil e posteriormente a variabilidade temporal por meio da técnica da análise harmônica, sendo para isso foi feito inicialmente uma análise de variância, fase e amplitude para o tempo presente (1980-2000) e, posteriormente, feita uma projeção com o tempo futuro (2080-2100), com base no cenário A2 do Painel Intergovernamental para as Mudanças Climáticas. A equação utilizada foi a de Penman-Monteith padronizada pela Food and Agriculture and Organization of the United Nations (FAO) 1998. As simulações foram conduzidas com o modelo regional de clima (MM5), acoplado a um modelo de vegetação potencial (MVP). Os resultados mostram que sob condições atuais o modelo apresentou bom desempenho do ciclo anual quando comparado aos dados do ERA-40 e CRU. Os termos aerodinâmico e radiativo apresentaram um ciclo anual que é dominante na região Amazônica e sul do Brasil, enquanto na região sudeste o ciclo semestral tem maior destaque. As maiores variações na amplitude da ETo foram identificadas no semi-árido nordestino e no extremo sul do Brasil. As mudanças na ETo devido ao aquecimento global foram máximas na região central do Brasil e Amazônica. Em condições futuras, o ciclo anual apresentou-se dominante na maior parte do Brasil, indicando estações secas e chuvosas de forma bem definida. Ainda foi observado que sob condições de aquecimento global as variações do termo aerodinâmico tornam-se mais importantes que as variações do termo radiativo para a ETo total.

Este trabalho apresenta o desenvolvimento e a implementação de um filtro ativo trifásico universal, o qual é composto pela conexão de três módulos monofásicos. Cada módulo monofásico é independente e é controlado por um processador digital de sinais. A estrutura de potência utilizada em cada módulo é uma topologia de três braços em que dois conversores compartilham um braço, de forma que o circuito apresenta número de componentes de potência reduzido na versão monofásica e pode operar sem o uso de um transformador. O filtro ativo proposto é capaz de compensar a distorção harmônica e regular o nível da tensão entregue para a carga. Ele também compensa a corrente da carga conectada na saída do filtro, corrigindo seu conteúdo harmônico e fator de potência. Apresenta-se uma revisão bibliográfica sobre alguns assuntos referentes à qualidade de energia elétrica, como os conceitos de distorção harmônica, seus efeitos e as normas pertinentes. Em seguida, as principais topologias de filtros ativos são apresentadas. Três módulos monofásicos, de 1500 W cada, são implementados e o funcionamento da estrutura de três braços, bem como os principais parâmetros do circuito de potência são analisados. Um algoritmo PLL (Phase Locked Loop) digital é empregado para o sincronismo de cada módulo. Controladores repetitivos são utilizados para o controle da tensão e da corrente. Os detalhes da estratégia de controle, bem como o projeto do circuito de sincronismo e dos controladores digitais são apresentados. Os resultados teóricos obtidos são comprovados através da simulação e da experimentação do protótipo implementado. A utilização do filtro ativo possibilitou a redução do conteúdo harmônico das cargas utilizadas nos testes, bem como elevou o fator de potência e corrigiu a distorção e o nível da tensão entregue para a carga. / This paper presents the development and implementation of a three-phase universal active filter consisting of three single-phase modules. Each single-phase module is independent and is controlled by a digital signal processor. The power structure used in each module is a three-arm topology in which two converts share one arm, so that the circuit has a reduced count of components and can operate without using a transformer. The proposed active filter can compensate harmonic distortion and adjust the voltage level delivered to the load. It also compensates the load current connected to the filter output, correcting its harmonic content and power factor. It presents a literature review on some issues related to power quality, as the concepts of harmonic distortion, its effects and relevant standards. Then the principal topologies used in active filters are presented. Three single-phase modules, each one of 1500 W, are implemented and the operation principles of the three-arms structure and the main parameters of the power circuit are analyzed. A digital PLL (Phase Locked Loop) is employed to synchronize each module. Repetitive controllers are used to control the voltage and current. Details of the control strategy and circuit design of the synchronism and digital controllers are presented. The results are verified through simulation and experimentation of the implemented prototype. Using the active filter was possible to reduce the harmonic content of the loads used in the experimental tests as well as increasing the power factor and to correct the distortion and voltage level supplied to the load.

CAPES / Este trabalho propõe uma modificação da meta-heurística Busca Harmônica (HS) a partir de uma nova abordagem baseada em população, empregando, também, algumas estratégias inspiradas em outras meta-heurísticas. Este novo modelo foi implementado utilizando a arquitetura de programação paralela CUDA em uma GPU. O uso de placas de processamento gráficas (GPU) para processamento de propósito geral está crescendo, e estas têm sido utilizadas por muitos pesquisadores para processamento científico. Seu uso se mostra interessante para meta-heurísticas populacionais, podendo realizar muitas operações simultaneamente. A HS é uma meta-heurística inspirada no objetivo de um músico em buscar uma harmonia perfeita. modelo proposto incluiu-se uma população de harmonias temporárias que são geradas a cada nova iteração, permitindo a realização simultânea de diversas avaliações de função. Assim aumenta-se o grau de paralelismo da HS, possibilitando maiores ganhos de velocidade com o uso de arquiteturas paralelas. O novo modelo proposto executado em GPU foi denominado Mega Harmony Search (MHS). Na implementação em GPU cada passo do algoritmo é tratado individualmente em forma de kernels com configurações particulares para cada um. Para demonstrar a eficácia do modelo proposto foram selecionados alguns problemas de benchmark, como a otimização de estruturas de proteínas, a otimização de treliças e problemas matemáticos. Através de experimentos fatoriais foi identificado um conjunto de parâmetros padrão, o qual foi utilizado nos outros experimentos. As análises realizadas sobre resultados experimentais mostram que o MHS apresentou solução de qualidade equivalente à HS e ganhos de velocidade, com a sua execução em GPU, superiores a 60x quando comparado a implementação em CPU. Em trabalhos futuros poderão ser estudadas novas modificações ao algoritmo, como a implementação de nichos e estudos de estratégias de interação entre eles. / This work propose a new approach for the metaheuristic Harmonic Search (HS), by using a population of solutiona and other strategies inspired in another metaheuristics. This new model was implemented using a parallel architecture of a graphical processing unity (GPU). The use of GPU for general-purpose processing is growing, specially for scientific processing. Its use is particularly interesting for populational metaheuristics, where multiple operations are executed simultaneously. The HS is a metaheuristic inspired by the way jazz musicians search for a perfect harmony. In the proposed model a population of temporary harmonies was included. Such population was generated at each iteration, enabling simultaneous evaluation of the objective function being optimized, and thus, increasing the level of parallelism of HS. The new approach implemented in GPU was named Mega Harmony Search (MHS), and each step of the algorithm is handled in the form of kernels with particular configurations for each one. To show the efficiency of MHS some benchmark problems were selected for testing, including mathematical optimization problems, protein structure prediction, and truss structure optimization. Factorial experiments were done so as to find the best set of parameters for the MHS. The analyzes carried out on the experimental results show that the solutions provided by MHS have comparable quality to those of the simple Harmony Search. However, by using GPU, MHS achieved a speedup of 60x, compared with the implementation in regular CPU. Future work will focus other improvements in the algorithm, such as the use of niches and species, as well a study of the interactions between them.

CAPES / Este trabalho propõe uma modificação da meta-heurística Busca Harmônica (HS) a partir de uma nova abordagem baseada em população, empregando, também, algumas estratégias inspiradas em outras meta-heurísticas. Este novo modelo foi implementado utilizando a arquitetura de programação paralela CUDA em uma GPU. O uso de placas de processamento gráficas (GPU) para processamento de propósito geral está crescendo, e estas têm sido utilizadas por muitos pesquisadores para processamento científico. Seu uso se mostra interessante para meta-heurísticas populacionais, podendo realizar muitas operações simultaneamente. A HS é uma meta-heurística inspirada no objetivo de um músico em buscar uma harmonia perfeita. modelo proposto incluiu-se uma população de harmonias temporárias que são geradas a cada nova iteração, permitindo a realização simultânea de diversas avaliações de função. Assim aumenta-se o grau de paralelismo da HS, possibilitando maiores ganhos de velocidade com o uso de arquiteturas paralelas. O novo modelo proposto executado em GPU foi denominado Mega Harmony Search (MHS). Na implementação em GPU cada passo do algoritmo é tratado individualmente em forma de kernels com configurações particulares para cada um. Para demonstrar a eficácia do modelo proposto foram selecionados alguns problemas de benchmark, como a otimização de estruturas de proteínas, a otimização de treliças e problemas matemáticos. Através de experimentos fatoriais foi identificado um conjunto de parâmetros padrão, o qual foi utilizado nos outros experimentos. As análises realizadas sobre resultados experimentais mostram que o MHS apresentou solução de qualidade equivalente à HS e ganhos de velocidade, com a sua execução em GPU, superiores a 60x quando comparado a implementação em CPU. Em trabalhos futuros poderão ser estudadas novas modificações ao algoritmo, como a implementação de nichos e estudos de estratégias de interação entre eles. / This work propose a new approach for the metaheuristic Harmonic Search (HS), by using a population of solutiona and other strategies inspired in another metaheuristics. This new model was implemented using a parallel architecture of a graphical processing unity (GPU). The use of GPU for general-purpose processing is growing, specially for scientific processing. Its use is particularly interesting for populational metaheuristics, where multiple operations are executed simultaneously. The HS is a metaheuristic inspired by the way jazz musicians search for a perfect harmony. In the proposed model a population of temporary harmonies was included. Such population was generated at each iteration, enabling simultaneous evaluation of the objective function being optimized, and thus, increasing the level of parallelism of HS. The new approach implemented in GPU was named Mega Harmony Search (MHS), and each step of the algorithm is handled in the form of kernels with particular configurations for each one. To show the efficiency of MHS some benchmark problems were selected for testing, including mathematical optimization problems, protein structure prediction, and truss structure optimization. Factorial experiments were done so as to find the best set of parameters for the MHS. The analyzes carried out on the experimental results show that the solutions provided by MHS have comparable quality to those of the simple Harmony Search. However, by using GPU, MHS achieved a speedup of 60x, compared with the implementation in regular CPU. Future work will focus other improvements in the algorithm, such as the use of niches and species, as well a study of the interactions between them.